Problem: The following line passes through point $(1, -6)$ : $y = -\dfrac{7}{2} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(1, -6)$ into the equation gives: $-6 = -\dfrac{7}{2} \cdot 1 + b$ $-6 = -\dfrac{7}{2} + b$ $b = -6 + \dfrac{7}{2}$ $b = -\dfrac{5}{2}$ Plugging in $-\dfrac{5}{2}$ for $b$, we get $y = -\dfrac{7}{2} x - \dfrac{5}{2}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(1, -6)$